Year: 2010
Type: book-chapter
Abstract: Quantum states are very delicate, so it is likely some sort of quantum error correction will be necessary to build reliable quantum computers.The theory of quantum error-correcting codes has some close ties to and some striking differences from the theory of classical error-correcting codes.Many quantum codes can be described in terms of the stabilizer of the codewords.The stabilizer is a finite Abelian group, and allows a straightforward characterization of the error-correcting properties of the code.The stabilizer formalism for quantum codes also illustrates the relationships to classical coding theory, particularly classical codes over GF(4), the finite field with four elements.To build a quantum computer which behaves correctly in the presence of errors, we also need a theory of fault-tolerant quantum computation, instructing us how to perform quantum gates on qubits which are encoded in a quantum errorcorrecting code.The threshold theorem states that it is possible to create a quantum computer to perform an arbitrary quantum computation provided the error rate per physical gate or time step is below some constant threshold value.
Author: Daniel Gottesman
Institution: University of Maryland, Baltimore County
Language: English
Subfield: Artificial Intelligence
Field: Computer Science
Domain: Physical Sciences
Open Access status: bronze
OpenAlex ID: W1675244148